Answer
$\log{2} +3\log{x} -2\log{y}$
Work Step by Step
Recall:
(1) Product Property of Logarithms: $\log_a{b}+\log_a{c}=\log_a{bc}$.
(2) Power Property of Logarithms: $\log_a{b^n} = n\cdot \log_a{b}$
Use the Product Property to obtain:
\begin{align*}
&=\log{2x^3} + \log{y^{-2}}\\
\end{align*}
Use the Power Property to obtain:
\begin{align*}
\log{2} + \log{x^3} + \log{y^{-2}}&=\log{2} +3\log{x} +(-2\log{y})\\
&=\log{2} +3\log{x} -2\log{y}
\end{align*}